LogCoshLoss

Log-Cosh Loss.

LogCosh(pred, target) = log(cosh(pred - target))

Log-cosh is approximately quadratic for small errors (like MSE) but behaves like L1 (MAE) for large errors, making it robust to outliers while still being twice differentiable everywhere.

Properties:

• log(cosh(x)) ≈ x²/2 for small x

• log(cosh(x)) ≈ |x| - log(2) for large |x|

This loss is smoother than Huber loss and doesn't have a non-differentiable point.